Entropic relations for indistinguishable quantum particles

Abstract

The von Neumann entropy of a k-body-reduced density matrix γ k quantifies the entanglement between k quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of k; it is concave for all 1⩽k⩽N and non-decreasing until the midpoint k⩽⌊N/2⌋ . The results hold for indistinguishable quantum particles and are independent of the statistics.